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Valuation of Convertible Bonds with Sequential Conversion

Abstract

In this paper, we characterize optimal conversion strategies and the related values of convertible bonds and stocks under a sequential conversion policy. Contrary to the existing literature, we consider firms that have both subordinated debt outstanding and convertible bonds. The additional debt results in wealth transfers among the holders of stock, convertible bonds, and additional debt, depending on the conversion strategy. These wealth transfers lead to remarkable differences in the optimal conversion policy and for the values of convertible bonds and stocks. It is possible that only a fraction of outstanding convertibles are converted at the last conversion date, that the stock value is partly strictly decreasing in the firm value, and partly decreasing in the dividend payment. It is also possible that certain stock values cannot occur when block conversion takes place, and that the value of a block-convertible bond is below and never above the corresponding value of a convertible bond under unresticted conversion.

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References

  • Barnea, Amir/Haugen, Robert A./Senbet, Lemma W. (1985), Agency Problems and Financial Contracting.

  • Black, Fischer/Cox, John C. (1976), Valuing Corporate Securities: Some Effects of Bond Indenture Provisions, in: The Journal of Finance, Vol. 31, pp. 351–367.

    Article  Google Scholar 

  • Black, Fischer/Scholes, Myron (1973), The Pricing of Options and Corporate Liabilities, in: The Journal of Political Economy, Vol. 81, pp. 637–654.

    Article  Google Scholar 

  • Blonski, Matthias (1999), Anonymous Games with Binary Actions, in: Games and Economic Behavior, Vol. 28, pp. 171–180.

    Article  Google Scholar 

  • Brennan, Michael J./Schwartz, Eduardo S. (1977), Convertible Bonds: Valuation and optimal Strategies for Call and Conversion, in: The Journal of Finance, Vol. 32, pp. 1699–1715.

    Article  Google Scholar 

  • Brennan, Michael J./Schwartz, Eduardo S. (1980), Analyzing Convertible Bonds, in: The Journal of Financial and Quantitative Analysis, Vol. 15, pp. 907–929.

    Article  Google Scholar 

  • Brennan, Michael J./Schwartz, Eduardo S. (1988), The Case for Convertibles, in: Journal of Applied Corporate Finance, Vol. 1, pp. 55–64.

    Article  Google Scholar 

  • Constantinides, George M. (1984), Warrant Exercise and Bond Conversion in Competitive Markets, in: Journal of Financial Economics, Vol. 13, pp. 371–397.

    Article  Google Scholar 

  • Constantinides, George M./Rosenthal, Robert W. (1984), Strategic Analysis of the Competitive Exercise of Certain Financial Options, in: Journal of Economic Theory, Vol. 32, pp. 128–138.

    Article  Google Scholar 

  • Crouhy, Michel/Galai, Dan (1994), The interaction between the financial and investment decisions of the firm: the case of issuing warrants in a levered firm, in: Journal of Banking and Finance, Vol. 18, pp. 861–880.

    Article  Google Scholar 

  • Emanuel, David C. (1983), Warrant Valuation and Exercise Strategy, in: Journal of Financial Economics, Vol. 12, pp. 211–235.

    Article  Google Scholar 

  • Fan, Hua/Sundaresan, Suresh (2000), Debt valuation, Strategic debt service and optimal dividend policy, in: Review of Financial Studies, Vol. 13, pp. 1057–1099.

    Article  Google Scholar 

  • Galai, Dan/Schneller, Meir I. (1978), Pricing Warrants and the Value of the Firm, in: The Journal of Finance, Vol. 33, pp. 1333–1342.

    Article  Google Scholar 

  • Geske, Robert (1977), The valuation of corporate liabilities as compound options, in: Journal of Financial and Quantitative Analysis, Vol. 12, pp. 541–552.

    Article  Google Scholar 

  • Ingersoll, Jonathan E. (1977), A Contingent-Claims Valuation of Convertible Securities, in: Journal of Financial Economics, Vol. 4, pp. 289–322.

    Article  Google Scholar 

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For valuable comments, we are grateful to Matthias Blonski, Peter Sauerbier, Rainer Schøbel, Suresh Sundaresan, Marliese Uhrig-Homburg, Josef Zechner, the participants of the theory workshop of the Department of Economics at the University of Mannheim, and the participants of the eighth annual meeting of the German Finance Association (DGF). For important improvements, we thank an anonymous referee.

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Bühler, W., Koziol, C. Valuation of Convertible Bonds with Sequential Conversion. Schmalenbach Bus Rev 54, 302–333 (2002). https://doi.org/10.1007/BF03396658

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  • DOI: https://doi.org/10.1007/BF03396658

JEL-Classification

  • G12
  • G13
  • G32